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A096697 Balanced primes of order five.

%I A096697 #29 Feb 16 2024 10:04:57
%S A096697 53,89,157,421,433,823,991,1297,1709,1873,2347,2411,2441,2729,2797,
%T A096697 3617,4793,5059,5417,6343,6781,7583,7933,8581,8861,9029,9857,11213,
%U A096697 11953,12329,13229,14081,14411,15767,15889,16561,16889,17029,20297,22469
%N A096697 Balanced primes of order five.
%H A096697 Aaron Toponce, <a href="/A096697/b096697.txt">Table of n, a(n) for n = 1..1000</a>
%e A096697 53 is a member because 53 = (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11. 53 is also an order one balance prime (A006562) and an order three balanced prime (A082078), thus it has an balanced index of three (A096707).
%t A096697 Transpose[ Select[ Partition[ Prime[ Range[5000]], 11, 1], #[[6]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[7]] + #[[8]] + #[[9]] + #[[10]] + #[[11]])/10 &]][[6]]
%t A096697 (* Second program: *)
%t A096697 With[{k = 5}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[3000], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]] (* _Michael De Vlieger_, Feb 15 2018 *)
%o A096697 (GAP) P:=Filtered([1..70000],IsPrime);;
%o A096697 a:=List(Filtered(List([0..3000],k->List([6..16],j->P[j-5+k])),i->
%o A096697 Sum(i)/11=i[6]),m->m[6]); # _Muniru A Asiru_, Feb 14 2018
%o A096697 (PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 5, sum(i=k-5, k+5, prime(i)) == 11*p;););} \\ _Michel Marcus_, Mar 07 2018
%Y A096697 Cf. A096693, A006562, A082077, A082078, A082079, A096698, A096699, A096700, A096701, A096702, A096703, A096704.
%K A096697 nonn
%O A096697 1,1
%A A096697 _Robert G. Wilson v_, Jun 26 2004